(WEAK) INCIDENCE BIALGEBRAS OF MONOIDAL CATEGORIES
نویسندگان
چکیده
منابع مشابه
Weak Hopf Monoids in Braided Monoidal Categories
We develop the theory of weak bimonoids in braided monoidal categories and show them to be quantum categories in a certain sense. Weak Hopf monoids are shown to be quantum groupoids. Each separable Frobenius monoid R leads to a weak Hopf monoid R ⊗ R.
متن کاملTannaka Reconstruction of Weak Hopf Algebras in Arbitrary Monoidal Categories
We introduce a variant on the graphical calculus of Cockett and Seely[2] for monoidal functors and illustrate it with a discussion of Tannaka reconstruction, some of which is known and some of which is new. The new portion is: given a separable Frobenius functor F : A −→ B from a monoidal category A to a suitably complete or cocomplete braided autonomous category B, the usual formula for Tannak...
متن کاملHochschild Cohomology of Algebras in Monoidal Categories and Splitting Morphisms of Bialgebras
Let (M,⊗,1) be an abelian monoidal category. In order to investigate the structure of Hopf algebras with Chevalley property (i.e. Hopf algebras having the coradical a Hopf subalgebra) we define the Hochschild cohomology of an algebra A in M. Then we characterize those algebras A which have dimension less than or equal to 1 with respect to Hochschild cohomology. We use these results to prove tha...
متن کاملAutonomization of Monoidal Categories
We define the free autonomous category generated by a monoidal category and study some of its properties. From a linguistic perspective, this expands the range of possible models of meaning within the distributional compositional framework, by allowing nonlinearities in maps. From a categorical point of view, this provides a factorization of the construction in [Preller and Lambek, 2007] of the...
متن کاملMonoidal Model Categories
A monoidal model category is a model category with a closed monoidal structure which is compatible with the model structure. Given a monoidal model category, we consider the homotopy theory of modules over a given monoid and the homotopy theory of monoids. We make minimal assumptions on our model categories; our results therefore are more general, yet weaker, than the results of [SS97]. In part...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2020
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089520000075